<p>This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.</p>

The purpose of this narrative inquiry study was to investigate the influence of curricular mandates on the teaching practices of high school mathematics teachers. Narrative inquiry, philosophically based on John Dewey’s theory of experience (Dewey, 1938), provides the intimate study of an individual's experience over time and in context(s) (Clandinin & Connelly, 2000). This study focused on the experiences of three high school mathematics teachers’ stories of educational change with data collected through interviews and personal documents. Socio-cultural narrative analysis was used to interpret the participants’ stories of adaptation. The data, presented as an ethnodrama, is composed of scenes taken from the interviews and interweaves the participants’ stories of evolution as they tackled the struggles of change on multiple levels: curriculum, student assessment, and teacher evaluation. Results indicated teachers adopt both traditional and reform strategies when deciding on appropriate teaching practices. Collaboration and professional development were two important aspects used by the participants to enlarge their toolbox of teaching practices when forced to challenge their existing beliefs. This study contributes to the scarce research on the impact of curricular mandates on teaching practices. It also highlights the experiences of high school mathematics teachers as they embrace the paradigm shift associated with the mandates and implement changes to their practices to promote a more student-centered, collaborative environment.

It is the purpose of this study to review in brief the changes that have taken place since the turn of the century in content of mathematical studies in the high school and to examine theoretically the significance of such changes.

The MA thesis focuses on the strategies pupils use when solving mathematical problems involving systems of linear equations in other subjects, namely in physics and chemistry. Drawing on the results of the experiment, the aim of the thesis is to propose ways in which these problems can be used in math lessons. The first part of the thesis is dedicated to those branches of physics and chemistry in which systems of linear equations are used. In the following part, the experiment itself is described. Divided into two parts, the first part of the experiment focuses on pupils at lower secondary schools, the other on pupils at upper secondary schools. The final part of the thesis is dedicated to suggesting how problems from physics and chemistry can be used in math lessons when introducing and practising systems of linear equations. Powered by TCPDF (www.tcpdf.org)

This thesis is focused on the utilization of simplified functional equations in logarithm exercise. The goal of this work is to assess the degree of formalism in the logarithm knowledge of high school students. The first part attends to the origin and development on the term logarithm and logarithmic tables. These findings are subsequently put into the context of present day logarithm teaching extracted from contemporary high school textbooks. The second part describes an experiment which was conducted for the purpose of this thesis. The final part contains the results of the thesis and the evaluation of their relevance for logarithm tuition. Keywords: logarithm, logarithm tables, textbook analysis, functional equations.

Results of researches on the popularity of mathematics point to the trend of decreasing popularity with the pupils' progression. According to the study of Chvál a stronger decline occurs between the fifth and sixth grades. The presented thesis focuses mainly on what factors of the transition of pupils from the primary to lower-secondary level can influence their attitudes towards mathematics and also on what causes the changes of these attitudes can be named by the pupils of the sixth year. It focuses not only on changes in relation to mathematics, but it also maps the solidarity with the teacher as well as pupils' self- confidence. The research is also concerned with possible changes in the relationship of pupils to mathematics depending on whether they are taught by the Hejny method or not. The research was carried out in the form of questionnaires mapping pupils' attitudes to mathematics and interviews with selected pupils of the schools participating in the research. The sample consisted of 235 pupils in five elementary schools. The complete data was obtained from 161 of them and this data is therefore a substantial part of the results analysis. The results confirmed that the pupils' relationship to mathematics deteriorated on average from primary to lower-secondary level. However, there are classes...

This study uses a discourse analysis from the perspectives of James Paul Gee (2005; 1999) in order to establish a socio-situated view of why grade 10 students often experience difficulties in representing mathematical word problems into appropriate equations and expressions that enable a solution to the problems. A discursive methodology was used to throw light on the difficulties that students experience that was different from the perspectives adopted previously, viz. from a view of the structure of the problems, from a pedagogic point of view and a cognitive understanding. An initial case study in one school in which four students were selected revealed that a master model existed that students were enacting when doing and talking about their experiences with word problems, viz. that word problems are obfuscatory. This master model rendered the students relatively mathematically helpless within a Discourse of school mathematics word problems. In order to more fully understand these findings an extended study was set up in which the methodology and analytic framework were refined. This extended study saw four students at each of three different sites selected to participate. The findings of this extended study were that the students enacting a situated Discourse model were more enabled within the Discourse of school mathematics word problems, whilst those enacting a deficit Discourse model were either peripheral or outside of that Discourse. This study contributes in that the constructs for the phenomena and the analytic tools within the context of school mathematics needed to be pioneered, adapted and refined over a period of time to address aspects particular to school mathematics. This resulted in a view from a socio-situated perspective which saw a shift in seeing what students do with the problem to what students do in the social setting associated with the problem. From this shift in focus came a new understanding of student difficulties with word problems that gave rise to a sub-Discourse within the Discourse surrounding school mathematics word problems, and students finding themselves in this sub-Discourse becoming marginalised through enacting a deficit Discourse model because they are unable to ascribe to the success model, or situated Discourse model.

Este trabalho tem o objetivo de verificar como o logaritmo e a função logarítmica são abordados nos livros didáticos de Matemática do século XIX ao XXI, indicando a inserção desses conteúdos na Matemática Escolar brasileira. Baseamo-nos, dentre outros autores, em Choppin (2004), Valente (1999, 2004, 2005 e 2008) e Bittencourt (2004 e 2008) para identificarmos o livro didático como fonte de pesquisa da Matemática Escolar, a partir de suas formas conceituais, de enfoque didático ou referente à organização do saber. A fim de verificar relações entre o histórico dos logaritmos e da função logarítmica na Matemática e na Matemática Escolar, apresentamos a ideia dos logaritmos de Napier como facilitadores de cálculos, interpretamos sua definição geométrica por meio de um sistema de equações diferenciais ordinárias e, assim, mostramos um breve histórico sobre a inserção do logaritmo como função no Cálculo Integral. Os livros didáticos de Matemática analisados foram publicados entre os anos de 1879 e 2013. Nesta análise, consideramos o modo como os autores abordam ou tratam a Matemática, os tipos de atividades que são propostas, os tipos de explicações, definições, exemplos, gráficos, exercícios, aplicações e problemas associados aos logaritmos e à função logarítmica. Os resultados apontam que no século XIX os logaritmos eram tratados nos livros didáticos, quase sempre, por meio da Aritmética. A partir da década de 1890, eles são abordados, tanto no campo aritmético, pela associação à teoria das progressões, como no campo algébrico, sendo expoentes numa equação ou função. A partir da década de 1930 até os dias de hoje verificamos uma predominância da concepção algébrico-funcional dos logaritmos. Com base nas Orientações Curriculares para o Ensino Médio (2006), nos Parâmetros Curriculares Nacionais Ensino Médio (PCNs - 2000), nos Parâmetros Curriculares Nacionais+ Ensino Médio (PCNs+ Ensino Médio - 2002), no Exame Nacional do Ensino Médio e em livros didáticos recentes, verificamos que os logaritmos e a função logarítmica se inserem, atualmente, na Matemática Escolar brasileira, pela sua associação às aplicações, como por exemplo, juros compostos, dinâmica populacional, desintegração radioativa, potencial hidrogeniônico, Escala Richter, Escala de Magnitude de Momento (MMS) e nível de intensidade sonora. / This work aims to verify how the logarithm and logarithmic function are approached in the textbooks of Mathematics from the 19th to the 21st century, indicating the insertion of these contents in Brazilian School Mathematics. We are based, among other authors, in Choppin (2004), Valente (1999, 2004, 2005 and 2008) and Bittencourt (2004 and 2008) to identify the didactic book as a research source of School Mathematics, from its conceptual forms, of didactic approach or referring to the organization of knowledge. In order to verify relations between the logarithmic and logarithmic functions in Mathematics and School Mathematics, we present the idea of the logarithms of Napier as facilitators of calculations, we interpret their geometric definition by means of a system of ordinary differential equations and we show a brief history about the insertion of the logarithm as a function in the Integral Calculus. The mathematical textbooks analyzed were published between the years 1879 and 2013. In this analysis, we consider how authors approach or treat mathematics, the types of activities that are proposed, the types of explanations, definitions, examples, graphs, exercises, applications and problems associated with logarithms and logarithmic function. The results show that in the 19th century, logarithms were treated in textbooks, almost always, through Arithmetic. From the 1890s, they are approached, both in the arithmetic field, by association with the theory of progressions, and in the algebraic field, being exponents in an equation or function. From the 1930s to the present day we have found a predominance of the algebraic-functional conception of logarithms. Based on the Curriculum Guidelines for Secondary Education (2006), the National Curriculum Parameters - Secondary Education (PCN\'s - 2000), the National Curriculum Parameters + High School (PCN\'s + High School - 2002), the National High School Examination and textbooks recent, we have verified that the logarithms and the logarithmic function are currently inserted in Brazilian School Mathematics, by their association to the applications, such as compound interest, population dynamics, radioactive disintegration, hydrogen ionic potential, Richter Scale, Momentum Magnitude Scale (MMS) and level of sound intensity.

Made available in DSpace on 2015-03-04T21:16:48Z (GMT). No. of bitstreams: 0 Previous issue date: 22 / Nenhuma / A Tese tem por objetivo problematizar um enunciado que circula de forma recorrente no discurso da Educação Matemática Escolar, que diz respeito à importância de trabalhar com a “realidade” do aluno. O material de pesquisa analisado abrange a Revista do Ensino do Rio Grande do Sul, especificamente os exemplares publicados entre os anos de 1939 e 1941, os anais dos três congressos brasileiros de Etnomatemática (CBEm’s) e os dos três últimos Encontros Nacionais de Educação Matemática (ENEM’s). Servindo-se das teorizações de Michel Foucault, do segundo Wittgenstein e de John Dewey, a Tese examina como foram sendo concebidas as relações entre a escola e o mundo social mais amplo no campo educacional do Ocidente e os entrelaçamentos do enunciado estudado com outros desse campo, que, em sua dispersão, acabaram por produzir efeitos de verdade no discurso da Educação Matemática Escolar. O trabalho investigativo mostrou: a) como o enunciado estudado foi sendo reatualizado ao atravessar os séculos XVII e XVIII, não se / The thesis aims to problematize a statement that circulates in a recurrent way in the School Mathematics Education discourse, which concerns the importance of working with the student’s “reality”. The data of the study comprises the Revista do Ensino do Rio Grande do Sul (Rio Grande do Sul State Teaching Journal), specifically the issues published between 1939 and 1941, the proceedings of the three Brazilian Congresses on Etnomathematics (CBEm’s) and the three last National Meetings on Mathematics Education (ENEM’s). Based on Michel Foucault, later Wittgenstein and John Dewey’s theorizations, the thesis examines how, in the Western educational field, the relationships between the school and the wider social world were being conceived and the intertwinements of the studied statement with others of such field, which, in their dispersion, produced effects of truth in the School Mathematics Education discourse. The investigation shows: a) how the statement under study was being renewed through the seventeenth an

Thesis (M.A. (Mathematics Education)) --University of Limpopo, 2013 / This study intended to improve Grade 9 learners’ mathematical processes of solving word problems. It was an action research study in my own classroom consisting of 64 Grade 9 learners. Learners were given learning activities on word problems to carry out as part of their normal classroom mathematics’ lessons. Data were collected in two stages: first, through passive observation, that is, without my intervention, and later through participant observation thus provoking their thinking as they attempt the given questions. The learners’ responses were analyzed through checking the mathematical processes they used without my intervention. Learners also submitted their post-intervention responses for analysis of progress after interventions. The scripts were reviewed based on four problem- solving stages adopted from George Polya (1945). Those stages are, namely understanding the problem, devising the plan, carrying out the plan and looking back. It became evident from the findings that learners attempt solving word problems with no understanding. Communication, reasoning and recording processes appear to be key factors in assisting learners to make sense of word problems and, finally, proceeding towards an adequate solution.